Parts: 3 4 3 [over] 2 1 8

3 2

[marginal figures: 1 1; b 2; 1 3; 16 16 t s 3 3; 120 16; r; o; 3 3; 120 8; f n; 1; m; 2; a; 1; 120; 7; 16; 4; 120; 15; 88; 8; 1 120; 2.] And 3/8 of n are truly the counterweight of b. Now find in that b the counterweight of the 3/8, which is simple friction; and let there remain over it so much weight that it makes a counterweight to itself. At the pivot n and at the weight a there are 4 pounds, of which I set its friction-portion at a quarter, of which I will place one at m. Therefore one at m and 2 at a make 3, which 3 wants its half, that is 1 and 1/2 at b, because the double arm is half weaker than its opposite, and so here the two opposing forces remain in equal powers. Now that 1 1/2 too sends the friction of its quarter to the said pivot and no more, and although it is twice as remote as the opposite arm of the friction, no account is taken of it here, because the weight b is balanced by the opposing power at m. Therefore, 3/8 being the quarter of the said weight of b, we must seek a weight equal to the friction arising from the 3/8 of n, which weight will be by half, because placed at double the distance from the center of the pivot than is the end of the arm of the friction. Therefore 3/16 will stand at p against 3/8 of n; and because these 3/16 also have their friction, and being in the same place as the 1 1/2 of b, they too must have their quarter sent to the friction; and just as resistance was made to the 3/8 of b with the half at p, that is 3/16, so to the friction of those 3/16, which is the quarter of their weight, that is 3/64, it will be resisted with the half at t, that is with 320 at [t].

3 / 2 / 1 3 1 / 4 4 / 3 2 / 1 3 / 4 4 / weight weight

[marginal figures] 3/64 3/8 ... 8; 3 3 3 3; 1 1/2; 1; 120 120 120 16; 1/8 3/8; 8 8 1 1/2; 1/16 3/16; 16; 8; 9; 16; 2; 18; 1/128 ...; 8 8; 120; 16; 8; 8; 960.

For making passementerie (braid / trimmings).

width ab - ab 8; thickness 8; 8. The friction of any body variously sided will always be equal resistance, on whichever side it is made, provided it does not dig into the plane on which it rubs. Every rubbed body resists on the site where it rubs by a fourth part of its weight. The friction of a heavy body will be of as much power when created by rolling around as along a plane. The modes of friction are of 3 kinds, of which one is caused by a straight flat surface, another by a curved one, as are pivots, and the third is made on a flat circle, as the millstone of mills. And from these arise 2 mixed and compound kinds, that is, one can partake of the first and third, the other of the first and second. There is the intersecting friction, which is two long bodies that move crosswise, and there is another in which the plane moves against the moving body that rubs upon it from above. The frictions of bodies are of as many various powers as are the varieties of the slipperiness of the bodies that rub together. The friction of bodies divides into 2 principal kinds, namely: liquid with liquid and dense with dense. From these arises a third kind which partakes of, or is composed of, the two aforesaid, that is, one can rub the liquid upon the dense and the dense upon the liquid, that is, the 'frictionable'. There is a fourth friction, among which is the wheel of the cart that moves over the ground, which does not rub but touches, and may be said to be of the nature of walking with steps of infinite smallness or minuteness. The frictional motions are of 2 kinds, that is flat and oblique, and never toward the center of the world except by accident.

a - n